Accurate raman spectroscopy

ABSTRACT

A method, a system, and a non-transitory computer readable medium for Raman spectroscopy. The method may include determining first acquisition parameters of a Raman spectroscope to provide a first acquisition set-up, the determining is based on at least one expected radiation pattern to be detected by a sensor of the Raman spectroscope as a result of an illumination of a first area of a sample, the first area comprises a first nano-scale structure, wherein at least a part of the at least one expected radiation pattern is indicative of at least one property of interest of the first nano-scale structure of the sample; wherein the first acquisition parameters belong to a group of acquisition parameters; setting the Raman spectroscope according to the first acquisition set-up; and acquiring at least one first Raman spectrum of the first nano-scale structure of the sample, while being set according to the first acquisition set-up

BACKGROUND

Raman Spectroscopy is an established technology, with extensiveliterature describing its usage for the characterization of variousmaterial properties.

The Raman spectrum carries information on various properties of asample. Most notably, different peaks in the spectrum correspond todifferent materials. When the measured target is comprised of materialcompounds (e.g. SiGe), specific peaks in the Raman spectrum wouldcorrespond to different atom pairs (e.g. Si—Si, Si—Ge and Ge—Ge).

Methods for extracting information on concentration and stress from thepositions of these peaks are well known in the literature. For example,a set of equations relating the positions of the three SiGe peaks withthe Germanium composition and the layer stress, is presented in thefollowing publication: T. S. Perov et al., Composition and strain inthin Sii-xGex virtual substrates measured by micro-Raman spectroscopyand x-ray diffraction, J. App. Phys. 109, 033502 (2011).

Doping is another characteristic which affects the Raman spectrum.Carrier concentration, arising from the dopant distribution, affects theRaman signal and causes an additional shift in the Raman peaks. Thelevel of doping can hence be incorporated into the fitting procedure,and concurrent assessment of doping level along with stress andcomposition is possible through monitoring peak locations (see forexample—A. Perez-Rodriguez et al., Effect of stress and composition onthe Raman spectra of etch-stop SiGeB layers, J. Appl. Phys. 80, 15(1996).

Examples of state of the art systems that generate Raman spectrums areprovided in PCT patent applications publication serial numbersWO2017/103934 of Barak et el. and WO2017/103935 of Barak et al., bothapplications are incorporated herein by reference.

In common Raman spectroscopy the image on the spectrometer is of theRaman spectrum at various wavelengths only and at a single illuminationdirection—which reduces the information that can be obtained duringRaman spectroscopy.

SUMMARY

There may be provided a system, a method and a non-transitory computerreadable medium that stores instructions for accurate Ramanspectroscopy.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to understand the invention and to see how it may be carriedout in practice, a preferred embodiment will now be described, by way ofnon-limiting example only, with reference to the accompanying drawings:

FIG. 1 illustrates an example of some elements of the opticalmeasurement system;

FIG. 2 illustrates examples of illuminating a sample from differentangles;

FIG. 3 illustrates examples of changing an angle of illumination;

FIG. 4 illustrates examples of electrical field distributions;

FIG. 5 illustrates examples of collecting radiation from differentangles;

FIG. 6 illustrates an example of some elements of the illuminationoptics;

FIG. 7 illustrates examples of different orientation of a dove prism andthe mapping between light from horizontal points and their projection ingeometric points;

FIG. 8 illustrates examples of a slit and a collection aperture;

FIG. 9 illustrates examples of signals formed on a sensor at differentphonon modes;

FIG. 10 is an example of an optical measurement system;

FIG. 11 is an example of an optical measurement system;

FIG. 12 is an example of an optical measurement system; and

FIG. 13 illustrates an example of a method.

DETAILED DESCRIPTION OF THE DRAWINGS

In the following detailed description, numerous specific details are setforth in order to provide a thorough understanding of the invention.However, it will be understood by those skilled in the art that thepresent invention may be practiced without these specific details. Inother instances, well-known methods, procedures, and components have notbeen described in detail so as not to obscure the present invention.

The subject matter regarded as the invention is particularly pointed outand distinctly claimed in the concluding portion of the specification.The invention, however, both as to organization and method of operation,together with objects, features, and advantages thereof, may best beunderstood by reference to the following detailed description when readwith the accompanying drawings.

It will be appreciated that for simplicity and clarity of illustration,elements shown in the figures have not necessarily been drawn to scale.For example, the dimensions of some of the elements may be exaggeratedrelative to other elements for clarity. Further, where consideredappropriate, reference numerals may be repeated among the figures toindicate corresponding or analogous elements.

Any reference in the specification to either one of a system, a methodand a non-transitory computer readable medium should be applied mutatismutandis to any other of the system, a method and a non-transitorycomputer readable medium. For example any reference to a system shouldbe applied mutatis mutandis to a method that can be executed by thesystem and to a non-transitory computer readable medium that may storesinstructions executable by the system.

Because the illustrated at least one embodiment of the present inventionmay for the most part, be implemented using electronic components andcircuits known to those skilled in the art, details will not beexplained in any greater extent than that considered necessary asillustrated above, for the understanding and appreciation of theunderlying concepts of the present invention and in order not toobfuscate or distract from the teachings of the present invention.

Any number, or value illustrated below should be regarded as anon-limiting example.

There may be provided a system, a method, and a non-transitory computerreadable medium that stores instructions for accurate Ramanspectroscopy.

There may be provided a system, a method, and a non-transitory computerreadable medium that stores instructions for collection andinterpretation of angle resolved Raman scattered light from Raman-activematerials, micro-structures and nano-structures.

There may be provided a system, a method, and a non-transitory computerreadable medium that stores instructions that may obtain Raman spectraat different scattering angles.

There may be provided a system, a method, and a non-transitory computerreadable medium that stores instructions for illuminating the samplefrom different illumination angles, creating additional independentspectra.

There may be provided a system, a method, and a non-transitory computerreadable medium that stores instructions for using polarization optics,enabling control of illumination polarization continuously andextraction of specific Raman spectra at different polarizations.

There may be provided a system, a method, and a non-transitory computerreadable medium that stores instructions for performing further analysisof information retrieved from the illumination of the sample forunraveling critical quantities about the nano-structure materials anddimensions.

The terms “micro-scale” and “nano-scale” are used in an interchangeablemanner. Any reference to a nano-scale may be applied mutatis mutandis toa micro-scale. Nano-scale means having at least one dimension that mayrange between one tenth of a nanometer till one hundred nanometers.Micro-scale means having at least one dimension that may range betweenone tenth of a micron till one hundred microns.

FIG. 1 illustrates an example of some elements of the opticalmeasurement system.

FIG. 1 illustrates an example of a part 200 of an optical measurementsystem.

Part 200 allows to illumination sample 300 by a laser or other lightsource (or several light sources) from various angles and polarizationsand the collection of Raman scattered light from the sample from variousangles and polarizations.

Part 200 includes an illumination path that includes laser 201, fieldimaging path 202, entrance aperture stop 203, mirror 204, apertureimaging path 205, first illumination lens 206, illumination field stop207, second illumination lens 208, illumination polarizer 209, beamsplitter 210, illumination half wavelength plate (HWP) such as aillumination rotating HWP 211, objective aperture stop/back focal plane212, and objective lens 213.

The collection path (for collecting radiation from sample 214) includesobjective lens 213, objective aperture stop/back focal plane 212, beamsplitter 210, collection quarter wavelength plate (QWP) such ascollection rotating QWP 215, collection rotating polarizer 216,collection filter 217, first collection lens 218, first collection fieldstop 219, rotating dove prism 220, second collection lens 221,collection aperture stop 222, cylindrical lens 223, second field stop224, slit lens 225, slit 226 and optical unit 235.

The optical unit 235 may be an optical spectrometer.

In FIG. 1 the optical unit 235 is illustrated as including a grid(grating) 231, first mirror/lens 232 for directing radiation that passedthrough the region of interest onto the grid 231, second lens/mirror 233for directing light from grid 231 towards a detector 234.

The Illumination Path

The optical scheme in FIG. 1 describes two main imaging paths. First,the central imaging path follows a path of a collimated light beamexiting from a laser 201. The beam goes through entrance aperture stop203, and is reflected by mirror 204. The mirror 204 position may becontrolled by a linear motor or any other mechanical manipulator,causing a lateral shift in the reflected laser beam. The laser beam isthen focused by first illumination lens 206 onto illumination field stop207 and recollimated again by second illumination lens 208. It thanpasses through illumination polarizer 209 and is partially reflected bybeam splitter 210. The reflected light then goes through illuminationrotating HWP 211 which rotates the polarization. After passing thewaveplate, the light goes through a high NA (numerical aperture)objective lens 213 and is imaged on the plane of sample 214.

The second imaging path is wider that the first and illustrates theimaging of the entrance aperture stop 203 onto the objective aperturestop/back focal plane 212. This is done using the relay lenses (firstillumination lens 206 and second illumination lens 208). Themagnification between entrance aperture stop 203 and objective aperturestop/back focal plane 212 is a function of the focal lengths of firstillumination lens 206 and second illumination lens 208: M=f₂/f₁.

The Collection Path

After reaching the sample, light is scattered from it and goes throughthe objective and waveplate (thus, the polarization of Reighleyscattered light is rotated back to its original state). From there, itreaches the beam splitter 210, where part of the scattered light istransmitted and reaches collection rotating QWP 215, collection rotatingpolarizer 216 collection filter 217 that may be a long-pass filter whichfilters the Reighley scattered light and transmits only the Ramanscattered light. Then, using first collection lens 218, the light isfocused onto a conjugate plane where first collection field stop 219 islocated.

Close to the field stop there is a rotating dove prism 220, responsiblefor rotating the image of the aperture stop. After that, secondcollection lens 221 collimates the light again. The image of theobjective aperture stop/back focal plane 212 (rotated by the dove prism)is formed at the focal plane of second collection lens 221 on thecollection aperture stop 222. Following that, cylindrical lens 223focuses the light in one direction onto second field stop 224. At thissurface, the rays originating from the aperture stop are collimated inone direction. A slit lens 225 creates an image of the Raman scatteredlight on a slit 226, where one direction (x) holds information ondifferent field points and the other direction (y) holds information ondifferent angular (NA) points.

Angle of illumination (AOI) control.

By use of mirror (denoted 204 in FIG. 1—may be a motorized mirror), thesuggested system has the capability to change the angle of illuminationon the sample (see FIG. 2). Thus, different information can be extractedfrom the sample. For example, in most crystal materials differentphonons are sensitive to the direction of the incident electric field.By illuminating light mainly in normal direction (NA₀ 272 in FIG. 2),the electric field of linearly polarized light will be mostly in thedirection parallel to the sample's surface (e.g. Ex), exciting onephonon (in Silicon that will be LO Longitudinal Optic phonon). However,illuminating from a large angle (NA₊₁ or NA⁻¹ for example the NAsdenotes 271 and 273 in FIG. 2), some of the electric field is in the zdirection (Ez), i.e. parallel to the surface's normal, which excites adifferent phonon (in Silicon [100]: TO—Transverse optic) in addition tothe LO phonon. Exciting these different phonons can contribute, in casethe outcome Raman spectra in different angles is uncorrelated, i.e. eachspectrum is correlated to different parameters in the sample, or in caseone parameter requires information from both angles.

We suggest two methods to displace a beam by amount Δ_(light) (see FIG.3):

A. In reflection: using a linear motor to displace mirror 204 (FIG. 3)such that: Δ_(light)=x_(mirror) [1]

B. In refraction: tilting an optical plate of a transparent plate 204′instead of mirror such that a (t_(plate), n_(plate) and θ_(plate) arethe plate's thickness, refractive index and tilt angle, respectively):

$\begin{matrix}{\Delta_{light} = {t_{plate}\sin {\theta_{plate}\left\lbrack {1 - \frac{\cos \theta_{plate}}{\sqrt{n_{plate}^{2} - {\sin^{2}\theta_{plate}}}}} \right\rbrack}}} & \lbrack 2\rbrack\end{matrix}$

Both suggested methods A and B allow scanning only in one direction.scanning in the perpendicular direction can be done by:

a. In A: using another mirror rotated by 90 degrees relative to thecurrent mirrorb. In B: using another tilted plate or tilting the same plate in twoorthogonal anglesc. A composition of A and Bd. Rotating the sample

Thus, with AOI control at two axes, the electric field distribution 260in illumination is given by E_(ill)(x−r_(AOI) cos θ_(AOI), y−r_(AOI) sinθ_(AOI)) (see FIG. 4), where (x,y) is the objective aperture stationaryaxes and (r_(AOI), θ_(AOI)) are the polar coordinates of theillumination beam center (controlled via AOI such that Δ_(light)^((x))=r_(AOI) cos θA_(OI) and Δ_(light) ^((y))=r_(AOI) sin θA_(OI)).

Illumination Polarization Control

As described above and in FIG. 1, the combination of three elements:mirror 204, illumination polarizer 209, and illumination rotating HWP211, allow control of the polarization direction in illumination.

The illumination polarizer 209 could be a fixed element, its task is toincrease the contrast of polarized light before it reaches the sample.The direction of polarized light should be either ‘s’ or ‘p’ relative tothe beam splitter 210 before it reaches the sample, as any otherdirection will introduce elliptical polarization in reflection due todifference in Fresnel reflections (magnitude and phase) between ‘s’ and‘p’ polarized light. Thus, the illumination polarizer 209 could beadjusted by rotating about the optical axis to achieve maximum contrastin reflection from the beam splitter 210.

After reflection, the light reaches the illumination rotating HWP 211,which is positioned in a manner that its fast axis is at an angleϕ_(HWP) relative to the incident polarization. After crossing it, thepolarization is rotated by twice that amount, achieving an angle2ϕ_(HWP) relative the original polarization. Thus, with AOI andpolarization control, the illumination beam field distribution, upon theobjective's aperture stop is described by the following formula (seeFIG. 4):

$\begin{matrix}{{\overset{\rightarrow}{E}}_{illumination}^{(12)} = {{E_{0}\left( {{x - {r_{AOI}\cos \; \theta_{AOI}}},{y - {r_{AOI}\sin \; \theta_{AOI}}}} \right)}\begin{bmatrix}{\cos \left( {2\varphi_{HWP}} \right)} \\{\sin \left( {2\varphi_{HWP}} \right)}\end{bmatrix}}} & \lbrack 3\rbrack\end{matrix}$

Where E₀ (x, y) is the field distribution at the aperture plane beforethe AOI transformations and the superscript “12” indicates that this isthe field on the aperture stop at illumination. Upon crossing theobjective, each (x-y) point on the aperture is refracted in a differentangle, resulting in variations in polarization state when hitting thesample. These variations affect the intensity distribution andpolarization state of the incoherent scattered light from the sample.

This can be formulated as a general two-dimensional Stokes vector:

$\begin{matrix}{{\overset{\rightarrow}{S}}_{scattered}^{(12)} = {\begin{bmatrix}S_{0}^{(12)} \\S_{1}^{(12)} \\S_{2}^{(12)} \\S_{3}^{(12)}\end{bmatrix}\left( {x,y,r_{AOI},\theta_{AOI},\varphi_{HWP}} \right)}} & \lbrack 4\rbrack\end{matrix}$

Where S₀₋₃ (x, y, r_(AOI), θ_(AOI), ϕ_(HWP)) are real functions of x, y,r_(AOI), θ_(AOI) and ϕ_(HWP).

Collection polarization measurement: In collection, there are threeparticipating elements in evaluating polarization state (in thefollowing order, for an incoherent beam exiting the sample, neglectingthe effect of the objective and beam-splitter on the scattered light):the illumination rotating HWP 211, collection rotating QWP 215 andcollection rotating polarizer 216. For simplicity, the beam splitter's210 effect on polarization is neglected.

When the scattered light passes through the illumination rotating HWP211 it undergoes a phase difference between polarization components(same as in illumination). Thus, for the simple case of the scatteredlight polarization being equal to illumination polarization (the latterwas rotated by angle 2ϕ_(HWP) after crossing the ½ waveplate (HWP)),than in the return direction it is rotated in the opposite direction byan angle −2ϕ_(HWP), retrieving the original polarization above the ½waveplate (HWP). Using Muller calculus, the effect of the illuminationrotating HWP 211 on the scattered light is as follows:

$\begin{matrix}{{\overset{\rightarrow}{S}}_{scattered}^{(11)} = {{\begin{bmatrix}1 & 0 & 0 & 0 \\0 & {\cos \left( {4\varphi_{HWP}} \right)} & {\sin \left( {4\varphi_{HWP}} \right)} & 0 \\0 & {\sin \left( {4\varphi_{HWP}} \right)} & {- {\cos \left( {4\varphi_{HWP}} \right)}} & 0 \\0 & 0 & 0 & {- 1}\end{bmatrix}{\overset{\rightarrow}{S}}_{scattered}^{(12)}} = {\quad\begin{bmatrix}S_{0}^{(12)} \\{{{\cos \left( {4\varphi_{HWP}} \right)}S_{1}^{(12)}} + {{\sin \left( {4\varphi_{HWP}} \right)}S_{2}^{(12)}}} \\{{{\sin \left( {4\varphi_{HWP}} \right)}S_{1}^{(12)}} - {{\cos \left( {4\varphi_{HWP}} \right)}S_{2}^{(12)}}} \\{- S_{3}^{(12)}}\end{bmatrix}}}} & \lbrack 5\rbrack\end{matrix}$

After crossing illumination rotating HWP 211, the scattered light ispartially transmitted through the beam-splitter. Above it, two optionsare suggested for implementing polarization measurement/

A collection rotating polarizer 216 (angle ϕ_(CLP)) only, collectionrotating QWP 215 is) removed. In this case, {right arrow over(S)}_(scattered) ⁽¹⁶⁾ will be:

$\begin{matrix}{{\overset{\rightarrow}{S}}_{scattered}^{(16)} = {{\frac{1}{2}\begin{bmatrix}1 & {\cos \left( {2\varphi_{CLP}} \right)} & {\sin \left( {2\varphi_{CLP}} \right)} & 0 \\{\cos \left( {2\varphi_{CLP}} \right)} & {\cos^{2}\left( {2\varphi_{CLP}} \right)} & {\frac{1}{2}{\sin \left( {4\varphi_{CLP}} \right)}} & 0 \\{\sin \left( {2\varphi_{CLP}} \right)} & {\frac{1}{2}{\sin \left( {4\varphi_{CLP}} \right)}} & {\sin^{2}\left( {2\varphi_{CLP}} \right)} & 0 \\0 & 0 & 0 & 0\end{bmatrix}}{\overset{\rightarrow}{S}}_{scattered}^{(11)}}} & \lbrack 6\rbrack\end{matrix}$

Which allows extraction of all stokes parameters but S₃ ⁽¹²⁾. The stokesvectors for

$\varphi_{CLP} = {0\mspace{14mu} {and}\mspace{14mu} \frac{\pi}{2}}$

are (using equations [4]-[6] and dropping (x, y, r_(AOI), θ_(AOI),ϕ_(HWP))).

$\begin{matrix}{{\overset{\rightarrow}{S}}_{scattered}^{({16})} = {{{\frac{1}{2}\begin{bmatrix}1 \\{\pm 1} \\0 \\0\end{bmatrix}}\left( {S_{0}^{({11})} \pm S_{1}^{({11})}} \right)} = {{\frac{1}{2}\begin{bmatrix}1 \\{\pm 1} \\0 \\0\end{bmatrix}}I_{scattered}^{({16})}}}} & \lbrack 7\rbrack\end{matrix}$

Where (+) and (−) signs are for

${\varphi_{CLP} = {{0\mspace{14mu} {and}\mspace{14mu} \varphi_{CLP}} = \frac{\pi}{2}}},$

respectively. The intensity on the detector is:

I _(scattered) ⁽¹⁶⁾ =S ₀ ⁽¹²⁾(x,y,r_(AOI),θ_(AOI)ϕ_(HWP))±(cos(4ϕ_(HWP))S ₁ ⁽¹²⁾(x,y,r_(AOI),θ_(AOI),ϕ_(HWP))+sin(4ϕ_(HWP))S ₂ ⁽¹²⁾(x,y,r_(AOI),ϕ_(HWP)))  [8]

Thus, by measuring the intensity on the detector for

${\varphi_{CLP} = {0\mspace{14mu} {and}\mspace{14mu} \frac{\pi}{2}}},$

this configuration allows interpreting partial information on the Ramanscattered light (enabling to extract S₀ ⁽¹²⁾ and the summation cos(4ϕ_(HWP)) S₁ ⁽¹²⁾+ sin(4ϕ_(HWP)) S₂ ⁽¹²⁾).

B—In this option, the combination of the ¼ waveplate (QWP) and thecollection polarizer allows to receive the full Stokes vector of thescattered light. The waveplate is allowed to rotate with rotation angleϕ_(HWP) whereas the collection polarizer is stationary in either ‘p’ or‘s’ polarizations. After crossing both elements, {right arrow over(S)}_(scattered) ⁽¹⁶⁾ is (for horizontal polarizer):

$\begin{matrix}{{\overset{\rightarrow}{S}}_{scattered}^{(16)} = {{\frac{1}{2}\begin{bmatrix}1 & {\cos^{2}\left( {2\varphi_{QWP}} \right)} & {\frac{1}{2}{\sin \left( {4\varphi_{QWP}} \right)}} & {\sin \left( {2\varphi_{QWP}} \right)} \\1 & {\cos^{2}\left( {2\varphi_{QWP}} \right)} & {\frac{1}{2}{\sin \left( {4\varphi_{QWP}} \right)}} & {\sin \left( {2\varphi_{QWP}} \right)} \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}}{\overset{\rightarrow}{S}}_{scattered}^{(11)}}} & \lbrack 9\rbrack\end{matrix}$

Substituting [5] in [9] yields the intensity on the detector:

I _(scattered) ⁽¹⁶⁾ =S ₀ ⁽¹²⁾+cos²(2ϕ_(QWP))(cos(4ϕ_(HWP))S ₁⁽¹²⁾+sin(4ϕ_(HWP))S ₂ ⁽¹²⁾)+½ sin(4ϕ_(QWP))(sin(4ϕ_(HWP))S ₁⁽¹²⁾−cos(4ϕ_(HWP))S ₂ ⁽¹²⁾)−sin(2ϕ_(QWP))S ₃ ⁽¹²⁾  [10]

Angular Resolved Raman (ARS)

The suggested system enables one to retrieve information on the Ramanscattering distribution from different angles of the sample. In thatsense, the scattered light can be decomposed to a series of plane waves,where each of these plane waves is focused onto a distinct point on theobjective aperture stop/back focal plane 212 (see FIG. 5 with differentplane waves 274, 275 and 276—at the center and edges of the numericalaperture of the objective lens).

Using second collection lens 221 and slit lens 225, an image of theaperture plane is formed on collection aperture stop 222.

By using a dove prism 220, located between these lenses, and rotating itby angle θ_(DP) the collection aperture image on collection aperturestop 222 will be rotated by 2θ_(DP) (see FIG. 6).

Neglecting non-ideal imaging effects (such as optical aberrations), theaperture-stop images after passing through an unrotated (θ_(DP)=0°) androtated (θ_(DP)=22.5°) dove prism 261 and 262 are shown in FIG. 7 firstand right sides of the figure, respectively. The cylindrical lenscollects light from all adjacent horizontal points and focuses them ontoa single geometric point. Thus, a thin line is formed along the verticaldirection of the slit (y). For example, at θ_(DP)=0° points 5 through 9are imaged onto a single point on the slit center, whereas atθ_(DP)=22.5° (aperture rotates by 45°) points 4,7 and 10 are summed atthe center. Thus, if the intensity on the non-rotated aperture 212 isI⁽¹²⁾(x,y) (where (x, y) are the non-rotated coordinates) then therotated aperture image 222 is:

I ⁽²²⁾(x′,y′,θ _(DP))=I ⁽¹²⁾cos 2 θ_(DP) −y′ sin 2θ_(DP) ,x′ sin 2θ_(DP) +y′ cos 2 θ_(DP))  [11]

On the slit 226, after passing through both cylindrical and slit lenses,light rays along the ‘x’ axis are focused onto a single point.Therefore, the intensity distribution on the spectrometer's slit (I⁽²⁶⁾)is the accumulated intensity after integrating along the ‘x’ axis (thespectral direction):

I ⁽²⁶⁾(y′,θ _(DP))=∫I ⁽¹²⁾(x′ cos 2 θ_(DP) −y′ sin 2θ_(DP) ,x′ sin 2θ_(DP) +y′ cos 2 θ_(DP))*P(x′,y′,θ _(DP))dx′  [12]

Where P(x,y,θ_(DP)) is a known transfer function of the optical systemand (*) states convolution. By taking several measurements at variousrotation angles and using inversion formulas, one can reconstruct theoriginal intensity on the aperture I⁽¹²⁾(x,y).

For the simple case in which systematic effects are negligible,P(x^(′),y^(′),θ_(DP))=δ(x^(′), y′) (where δ(x, y) is delta function);thus, equation [12] is reduced to the known Radon transform andI⁽¹²⁾(x,y) is found through an inverse Radon transform:

$\begin{matrix}{{I^{({12})}\left( {x,y} \right)} = {\frac{1}{2\pi}{\int_{0}^{\pi}{{I^{({26})}\left( {{y^{\prime}\left( {x,y,\theta_{DP}} \right)},\theta_{DP}} \right)}*{g\left( {x,y,\theta_{DP}} \right)}d\; \theta_{DP}}}}} & \lbrack 13\rbrack\end{matrix}$

where y′(x,y,θ_(DP))=y cos 2 θ_(DP)−x sin 2 θ_(DP) andg(x,y,θ_(DP))=∫_(−∞) ^(∞)|r|e^(−iry′(x,y,θ) ^(DP) ⁾dr.

As an example to the benefit of the ARS technic, FIG. 9 shows theangular Raman scattering from Silicon substrate for Co-pol-0configuration (where Co-pol refers to the case in which ϕ_(CLP) equalsthe illumination polarization state on the sample and the ‘0’ means thatϕ_(HWP)=0). In that case, equation [8] is reduced to(r_(AOI)=θ_(AOI)=0):

I _(scattered) ⁽¹⁶⁾ =S ₀ ⁽¹²⁾(x,y,0,0,0)+S ₁ ⁽¹²⁾(x,y,0,0,0)  [14]

FIG. 9 illustrates examples of a silicon substrate has three differentphonons (two Transverse modes (TO) and one longitudinal mode (LO)) witha very distinctive and singular NA map for each phonon. On the detector,information from all three phonons will be collected simultaneously.

TO1 phonons have more intensity at the edges—radiation pattern 281 ofTO1 has regions of interest 282 at its edges centered at angles 45degrees, 135 degrees, 225 degrees and 315 degrees.

TO2 phonons have more intensity at the edges—radiation pattern 282 ofTO2 has regions of interest 285 at its edges centered at angles 90degrees and 270 degrees.

LO phonon is more evident at the aperture center—radiation pattern 283of LO has region of interest 288 at its center.

It should be noted that changes in one or more acquisition parametersmay change the radiation pattern.

Which radiation pattern is expected to obtain when illumination acertain location of a wafer and at certain acquisition parameters may berepresented by a model.

FIG. 9 illustrates that spatial filters (masks) 283, 286 and 289 may beare applied on the NA/aperture plane to mask irrelevant signals in eachone of TO0, TO1 and LO.

Thus, by measuring at two dome configurations, at

${\theta_{DP} = {0\mspace{14mu} {and}\mspace{14mu} \frac{\pi}{8}}},$

one can decouple the information of the TO phonons from that of themasking LO phonon.

Mask on the NA/Aperture Plain

An additional implementation of ARS is the use of spatial masks in theaperture plain 222 instead of the rotating dove prism 220 and thecylindrical lens 223. Using Raman modeling capabilities, we can simulatethe angular dependence of each vibrational mode. Different vibrationalmodes have different distributions along the aperture plain. Forexample, in FIG. 9 the angular distribution of the aperture plain of the2 Transverse modes (TO) and the longitudinal mode (LO) of bare Si inco-0 configuration is presented.

Using a mask will allow to block/pass specific modes of interest. Thereare several use cases for such a technique. For example to increase theextinction ratio (super nulling configuration) and increase thesensitivity to specific layers on top of the Si substrate. An additionalapplication is using these masks to couple to each mode (LO or TO) forstrain decomposition or to couple to different materials in the stack ofinterest.

FIG. 10 is an example of an optical measurement system 200.

Optical measurement unit 200 includes an illumination path, a collectionpath, a control unit and a mechanical movement unit 303 for supportingsample 300 and for moving the sample 300 in relation to the collectionand illumination paths. It should be noted that the sample 300 may bestatic while the illumination and/or collection paths may move. Itshould be noted that both the sample 300 and at least one path of thecollection and/or illumination may move in relation to each other.

In FIG. 10 the collection path and the illumination path share anobjective lens 213, and a half wavelength plate (HWP) 109. It should benoted that the illumination path and the collection path may share morecomponents, may share other components, or may not share any component.

In FIG. 10 the illumination angle and the collection angle areperpendicular to the sample. It should be noted that any otherillumination angles and/or collection angles may be provided.

The illumination path is configured to control various parameters of anillumination beam such as but not limited to polarization, frequencyspectrum, shape, size, coherency, path, intensity, and the like. Variouselements illustrated in the figure assist in the control of saidparameters. Elements that control polarizations are referred aspolarization control elements. Elements that control other parameters ofthe beam are referred to as additional control elements. It should benoted that a single element may control one or more parameters of thebeam. Non-limiting examples of elements include polarizers, halfwaveplates, quarter waveplates, analyzers, lenses, grids, apertures, andthe like.

The collection path is configured to control various parameters of theimpinging beam such as but not limited to polarization, frequencyspectrum, shape, size, coherency, path, intensity, and the like. Variouselements illustrated in the figure assist in the control of saidparameters.

The illumination path is illustrated as including (a) laser 102, (b)illumination optics 103 that include illumination polarization controlelement 103(1) and additional illumination control element 103(2), (c) abeam splitter such as dichroic beam splitter 210, (d) HWP 109, and (e)objective lens 213. The additional illumination control element maycontrol one or more parameters that differ from polarization for exampleshape, size, angle of propagation, and the like.

The collection path is illustrated as including (a) a beam splitter suchas dichroic beam splitter 210, (b) HWP 109, (c) objective lens 213, (d)collection optics 105 that include adjustable optics 105(1) for changingthe collection path thereby compensating for misalignments, additionalcollection control element 105(2), and collection polarization controlelement 105(3), (e) spatial filter 223, and (f) optical unit 235 (e.g.an optical spectrometer) that includes a grid/grating 231, firstlens/mirror 232 for directing radiation that passed through the regionof interest onto the grid 231, second lens/mirror 233 for directinglight from grid 231 towards detector 234.

The optical unit 235 is configurable in the sense that the spatialrelationship between the grid 231 and at least the second lens 233 maybe altered to direct different radiation lobes from the grid 231 towardsthe second lens 233. FIG. 4 (as well FIGS. 10 and 11) illustrates arotating unit 238 that may rotate the grid 231 in relation to the firstand second lenses. Movements other than rotations may be used to changethe spatial relationship between the elements of optical unit 235.

Detector 234 is configured to generate Raman spectra. The detector 234is coupled to control unit 239 that is configured to control variouscomponents/units/elements of the optical measurement system and may beconfigured to control the calibration process.

FIG. 11 is an example of an optical measurement system 200′.

Measurement system 200′ differs from measurement unit 200 by (a) notincluding HWP 109, (b) including multiple lasers 102′, and (c) includinga processing unit 234′ for processing detection signals. Theillumination optics 103 may be configured to combine or select radiationfrom the multiple lasers. In some cases only one laser may be activatedat a time.

FIG. 12 is an example of an optical measurement system 200″.

Measurement system 200″ differs from measurement unit 200 by (a)including multiple lasers 102′. The illumination optics 103 may beconfigured to combine or select radiation from the multiple lasers. Insome cases only one laser may be activated at a time.

FIG. 13 illustrates an example of a method 400.

Method 400 may include one or multiple iterations of steps 410, 420 and430.

Method 400 may start by step 410 of determining current acquisitionparameters of a Raman spectroscope to provide a current acquisitionset-up.

The determining is based on at least one expected radiation pattern tobe detected by a sensor of the Raman spectroscope as a result of anillumination of a first area of a sample.

The first area may include a first nano-scale structure.

At least a part of the at least one expected radiation pattern isindicative of at least one property of interest of the first nano-scalestructure of the sample.

The current acquisition parameters belong to a group of acquisitionparameters.

Step 410 may be based on a model that maps different acquisitionset-ups, to different expected radiation patterns. The model is merely anon-limiting example for predicting maps the relationship betweendifferent acquisition set-ups and different expected radiation patterns.

The group of acquisition parameters may include an illumination angle,an illumination polarization, a collection angle, a collectionpolarization, an illumination spatial masking and a collection spatialmasking.

At least one acquisition parameter may be changed between one iterationof steps 410, 420 and 430 to another iteration of steps 410, 420 and430.

Current acquisition parameters may include an illumination angle,wherein the setting comprises determining a position of a mirror of anillumination path of the Raman spectroscope

Current acquisition parameters may include an angular position of a doveprism of a collection path of the Raman spectroscope.

Current acquisition parameters may include a polarization set (provided,generated) by an optical module that may include an illuminationpolarizer, a rotating illumination half waveplate, and a rotatingcollection one fourth waveplate. Only a beam splitter may be positioned(a) in an optical path between the illumination polarizer and therotating illumination half waveplate, and (b) in another optical pathbetween the rotating collection one fourth waveplate and the rotatingillumination half waveplate.

Current acquisition parameters may include a location of a spatial mask.

Step 410 may be followed by step 420 of setting the Raman spectroscopeaccording to the current acquisition set-up.

Step 420 may be followed by step 430 acquiring at least one first Ramanspectrum of the first nano-scale structure of the sample, while beingset according to the current acquisition set-up.

Step 430 may include extracting different information regardingdifferent phonon modes.

Steps 410, 420, and 430 may be repeated multiple times. A currentiteration of steps 410, 420 and 430 may be repeated by a next iteration.This is illustrated by the dashed arrow from step 430 to step 410.

It should be noted that the analysis of radiation and/or a generating ofa Raman spectrum from detection signals of a detector and/or an analysisof a Raman spectrum to determine features of the objects may beexecuted, at least in part, by a controller and/or a processing circuitthat does not belong to the optical measurement system and/or may beremotely positioned from the illumination and/or collection paths.

There may be provided a method for Raman spectroscopy, the method mayinclude determining first acquisition parameters of a Raman spectroscopeto provide a first acquisition set-up, the determining may be based onat least one expected radiation pattern to be detected by a sensor ofthe Raman spectroscope as a result of an illumination of a first area ofa sample, the first area may include a first nano-scale structure,wherein at least a part of the at least one expected radiation patternmay be indicative of at least one property of interest of the firstnano-scale structure of the sample; wherein the first acquisitionparameters belong to a group of acquisition parameters; setting theRaman spectroscope according to the first acquisition set-up; andacquiring at least one first Raman spectrum of the first nano-scalestructure of the sample, while being set according to the firstacquisition set-up.

The group may include an illumination angle, an illuminationpolarization, a collection angle, a collection polarization, anillumination spatial masking and a collection spatial masking.

The first acquisition parameters may include an illumination angle,wherein the setting may include determining a position of a mirror of anillumination path of the Raman spectroscope.

The first acquisition parameters may include an angular position of adove prism of a collection path of the Raman spectroscope.

The first acquisition parameters may include a polarization set by anoptical module that may include an illumination polarizer, a rotatingillumination half waveplate, and a rotating collection one fourthwaveplate; wherein only a beam splitter may be positioned (a) in anoptical path between the illumination polarizer and the rotatingillumination half waveplate, and (b) in another optical path between therotating collection one fourth waveplate and the rotating illuminationhalf waveplate.

The first acquisition parameters may include a location of a spatialmask.

The acquiring may include extracting different information regardingdifferent phonon modes.

The determining may be based on a model that maps different acquisitionset-ups, to different expected radiation patterns.

The method may include determining second acquisition parameters of theRaman spectroscope to provide a second acquisition set-up, thedetermining may be based on at least one expected radiation pattern tobe detected by the sensor of the Raman spectroscope as a result of anillumination of a second nano-scale area of the sample, wherein at leasta part of the at least one expected radiation pattern may be indicativeof at least one property of interest of the second nano-scale area ofthe sample, the second acquisition parameters belong to the group;setting the Raman spectroscope according to the second acquisitionset-up; and acquiring at least one second Raman spectrum of the secondnano-scale area of the sample, while being set according to the secondacquisition set-up.

There may be provided an optical measurement system that may includeoptics, the optics may include an illumination path and a collectionpath; a Raman spectroscope; a controller that may be configured todetermine first acquisition parameters of a Raman spectroscope toprovide a first acquisition set-up, the determining may be based on atleast one expected radiation pattern to be detected by a sensor of theRaman spectroscope as a result of an illumination of a first area of asample, the first area may include a first nano-scale structure, whereinat least a part of the at least one expected radiation pattern may beindicative of at least one property of interest of the first nano-scalestructure of the sample; wherein the first acquisition parameters belongto a group of acquisition parameters; wherein the Raman spectroscope maybe arranged to be configured according to the first acquisition set-up;and wherein the optics may be configured to acquire at least one firstRaman spectrum of the first nano-scale structure of the sample, whilebeing set according to the first acquisition set-up.

The group may include an illumination angle, an illuminationpolarization, a collection angle, a collection polarization, anillumination spatial masking and a collection spatial masking.

The first acquisition parameters may include an illumination angle,wherein the setting may include determining a position of a mirror of anillumination path of the Raman spectroscope.

The first acquisition parameters may include an angular position of adove prism of a collection path of the Raman spectroscope.

The first acquisition parameters may include a polarization set by anoptical module that may include an illumination polarizer, a rotatingillumination half waveplate, and a rotating collection one fourthwaveplate; wherein only a beam splitter may be positioned (a) in anoptical path between the illumination polarizer and the rotatingillumination half waveplate, and (b) in another optical path between therotating collection one fourth waveplate and the rotating illuminationhalf waveplate.

The first acquisition parameters may include a location of a spatialmask.

The optics may be configured to extract different information regardingdifferent phonon modes.

The controller may be configured to determine based on a model that mapsdifferent acquisition set-ups, to different expected radiation patterns.

The controller may be configured to determine second acquisitionparameters of the Raman spectroscope to provide a second acquisitionset-up, the determining may be based on at least one expected radiationpattern to be detected by the sensor of the Raman spectroscope as aresult of an illumination of a second nano-scale area of the sample,wherein at least a part of the at least one expected radiation patternmay be indicative of at least one property of interest of the secondnano-scale area of the sample, the second acquisition parameters belongto the group; setting the Raman spectroscope according to the secondacquisition set-up; and wherein the optics may be configured to acquireat least one second Raman spectrum of the second nano-scale area of thesample, while being set according to the second acquisition set-up.

There may be provided a non-transitory computer readable medium thatstores instructions for: determining first acquisition parameters of aRaman spectroscope to provide a first acquisition set-up, thedetermining may be based on at least one expected radiation pattern tobe detected by a sensor of the Raman spectroscope as a result of anillumination of a first area of a sample, the first area may include afirst nano-scale structure, wherein at least a part of the at least oneexpected radiation pattern may be indicative of at least one property ofinterest of the first nano-scale structure of the sample; wherein thefirst acquisition parameters belong to a group of acquisitionparameters; setting the Raman spectroscope according to the firstacquisition set-up; and acquiring at least one first Raman spectrum ofthe first nano-scale structure of the sample, while being set accordingto the first acquisition set-up.

Any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality may be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermedial components. Likewise, any two components soassociated can also be viewed as being “operably connected,” or“operably coupled,” to each other to achieve the desired functionality.

Furthermore, those skilled in the art will recognize that boundariesbetween the above described operations merely illustrative. The multipleoperations may be combined into a single operation; a single operationmay be distributed in additional operations and operations may beexecuted at least partially overlapping in time. Moreover, alternativeembodiments may include multiple instances of an operation, and theorder of operations may be altered in various other embodiments.

Also for example, in one embodiment, the illustrated examples may beimplemented as circuitry located on a single integrated circuit orwithin a same device. Alternatively, the examples may be implemented asany number of separate integrated circuits or separate devicesinterconnected with each other in a suitable manner.

Also for example, the examples, or portions thereof, may implemented assoft or code representations of physical circuitry or of logicalrepresentations convertible into physical circuitry, such as in ahardware description language of any appropriate type.

However, other modifications, variations and alternatives are alsopossible. The specifications and drawings are, accordingly, to beregarded in an illustrative rather than in a restrictive sense.

In the claims, any reference signs placed between parentheses shall notbe construed as limiting the claim. The word ‘comprising’ does notexclude the presence of other elements or steps then those listed in aclaim. Furthermore, the terms “a” or “an,” as used herein, are definedas one or more than one. Also, the use of introductory phrases such as“at least one” and “one or more” in the claims should not be construedto imply that the introduction of another claim element by theindefinite articles “a” or “an” limits any particular claim containingsuch introduced claim element to inventions containing only one suchelement, even when the same claim includes the introductory phrases “oneor more” or “at least one” and indefinite articles such as “a” or “an.”The same holds true for the use of definite articles. Unless statedotherwise, terms such as “first” and “second” are used to arbitrarilydistinguish between the elements such terms describe. Thus, these termsare not necessarily intended to indicate temporal or otherprioritization of such elements. The mere fact that certain measures arerecited in mutually different claims does not indicate that acombination of these measures cannot be used to advantage.

While certain features of the invention have been illustrated anddescribed herein, many modifications, substitutions, changes, andequivalents will now occur to those of ordinary skill in the art. It is,therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the invention.

The terms “including”, “comprising”, “having”, “consisting” and“consisting essentially of” are used in an interchangeable manner. Forexample—any method may include at least the steps included in thefigures and/or in the specification, only the steps included in thefigures and/or the specification.

We claim:
 1. An optical measurement system as substantially illustratedin the specification.
 2. An optical measurement system as substantiallyillustrated in the drawings.
 3. A method as substantially illustrated inthe specification.
 4. A method as substantially illustrated in thedrawings.
 5. A non-transitory computer readable medium as substantiallyillustrated in the specification.